The Gorenstein projective modules for the Nakayama algebras. I

The aim of this paper is to outline the structure of the category of the Gorenstein projective Λ-modules, where Λ is a Nakayama algebra. In addition, we are going to introduce the resolution quiver of Λ. It provides a fast algorithm in order to obtain the Gorenstein projective Λ-modules and to decide whether Λ is a Gorenstein algebra or not, and whether it is CM-free or not.